• Title, Summary, Keyword: Nonlinear Vibration

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Forced Vibration Analysis for Duffing's Vibration Systems with the Multi-Degree-of-Freedom Systems (다자유도계를 갖는 듀핑 진동계의 강제진동해석)

  • 전진영;박용남;김정렬;김의간
    • Journal of Advanced Marine Engineering and Technology
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    • v.24 no.1
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    • pp.18-24
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    • 2000
  • As ship's propulsion shafting system has been complicated, many linear methods that have been used until now are not sufficient enough to produce proper solutions and these solutions are ofter unreasonable. So we need to solve nonlinear systems, and many methods for solving nonlinear vibration system have been developed. In this study, the propulsion shafting system was modeled with Duffing's nonlinear vibration system and multi-degree-of-freedom, and analyzed by using Quasi-Newton method. And for the purpose of confirming the reliability of the calculating results for nonlinear forced torsional vibration of the propulsion shafting system, the nonlinear calculated results were compared with the linear calculated ones for ship's propulsion shafting system. In the result, for analysis of the forced torsional vibration of the propulsion systems with nonlinear elements, the modified Newton's method is confirmed reasonable.

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Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects

  • Kunbar, Laith A. Hassan;Hamad, Luay Badr;Ahmed, Ridha A.;Faleh, Nadhim M.
    • Smart Structures and Systems
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    • v.25 no.5
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    • pp.619-630
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    • 2020
  • This paper studies nonlinear free vibration characteristics of nonlocal magneto-electro-elastic (MEE) nanobeams resting on nonlinear elastic substrate having geometrical imperfection by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All of previously reported studies on MEE nanobeams ignore the influences of geometric imperfections which are very substantial due to the reason that a nanobeam cannot be always perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric constituent in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam are dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and geometrical imperfection.

Development of the Optimal Design Technique for the Pneumatic Vibration Isolation System by Nonlinear Modeling and Analysis (공압방진시스템의 비선형 모델링과 해석을 통한 최적설계기술 개발)

  • 문준희;박희재
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.151-154
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    • 2001
  • The pneumatic vibration isolation systems have been widely used in industry and laboratories, but the full mathematical analysis and nonlinear modeling techniques have not been reported yet, even while the nonlinear features of the pneumatic vibration isolation system decide the main characteristics. For instance, the orifice in a pneumatic vibration isolator has been traditionally considered as a simple viscous damper, which was too much simplified to explain the performance of the isolation system. In this paper, the nonlinear characteristics are considered for the orifice and chamber, etc. The numerical simulation is carried out by the MATLAB/Simulink software. From the analysis result, a clear trend of the nonlinear features is shown: the vibration transmissibility changes not only due to the excitation frequency but also due to the amplitude of the vibration excitation. Therefore various design parameters are optimally chosen for the vibration isolation system. The proposed methods show good compatibility between the analysis results and the experiments.

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Nonlinear vibration analysis of composite laminated trapezoidal plates

  • Jiang, Guoqing;Li, Fengming;Li, Xinwu
    • Steel and Composite Structures
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    • v.21 no.2
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    • pp.395-409
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    • 2016
  • Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman's large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton's principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations

  • Akgoz, Bekir;Civalek, Omer
    • Steel and Composite Structures
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    • v.11 no.5
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    • pp.403-421
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    • 2011
  • In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.

Stochastic vibration response of a sandwich beam with nonlinear adjustable visco-elastomer core and supported mass

  • Ying, Z.G.;Ni, Y.Q.;Duan, Y.F.
    • Structural Engineering and Mechanics
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    • v.64 no.2
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    • pp.259-270
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    • 2017
  • The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

Identification of vibration System With Stiffness and Damping Nonlinearity (비선형 강성 및 감쇠 특성을 갖는 진동 시스템의 규명)

  • 이병림;이재응
    • Journal of KSNVE
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    • v.10 no.1
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    • pp.144-152
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    • 2000
  • The identification of a nonlinear vibration system based on the time domain parametric model has been widely studied in recent years. In most of the studies, the NARMAX model has been used for the identification of a nonlinear system. However, the computational load for the identification with this model is quite heavy. In this paper, a new modeling procedure for nonlinear system identification in discrete time domain is proposed. The proposed model has less initial nonlinear terms than NARMAX model, and the terms in the proposed model are derived from physically meaningful way. The performance of the proposed method is evaluated through the simulation, and the result shows that the proposed model can identify the nonlinear characteristics of the vibration system very will less computational effort.

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Nonlinear vibration characteristics of a vertical passive zero stiffness isolator (수직방향 수동 영강성 제진기의 비선형 진동 특성)

  • Kim, Kyoung-Hong;Ahn, Hyeong-Joon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.1259-1265
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    • 2007
  • This paper presents nonlinear vibration characteristics of a vertical passive zero stiffness isolator. The passive isolator can achieve zero stiffness through buckling of notched flexure caused by a compressive force. First, a simulation model of the isolator was built based on elastic beam theory. As increasing the compression force, time and frequency responses of the isolator were simulated. In addition, further nonlinear vibration characteristics were investigated through a bifurcation diagram and a Poincare's map, which shows that even chaostic vibration could happen. The simulations show that as the compressive force increases, the stiffness goes close to zero and the nonlinear characteristic becomes stronger to have a great effect on the isolation performance.

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Nonlinear vibration of hybrid composite plates on elastic foundations

  • Chen, Wei-Ren;Chen, Chun-Sheng;Yu, Szu-Ying
    • Structural Engineering and Mechanics
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    • v.37 no.4
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    • pp.367-383
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    • 2011
  • In this paper, nonlinear partial differential equations of motion for a hybrid composite plate subjected to initial stresses on elastic foundations are established to investigate its nonlinear vibration behavior. Pasternak foundation and Winkler foundations are used to represent the plate-foundation interaction. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the example problems. The governing equations of motion are reduced to the time-dependent ordinary differential equations by the Galerkin's method. Then, the Runge-Kutta method is used to evaluate the nonlinear vibration frequency and frequency ratio of hybrid composite plates. The nonlinear vibration behavior is affected by foundation stiffness, initial stress, vibration amplitude and the thickness ratio of layer. The effects of various parameters on the nonlinear vibration of hybrid laminated plate are investigated and discussed.

A nonlinear structural experiment platform with adjustable plastic hinges: analysis and vibration control

  • Li, Luyu;Song, Gangbing;Ou, Jinping
    • Smart Structures and Systems
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    • v.11 no.3
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    • pp.315-329
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    • 2013
  • The construction of an experimental nonlinear structural model with little cost and unlimited repeatability for vibration control study represents a challenging task, especially for material nonlinearity. This paper reports the design, analysis and vibration control of a nonlinear structural experiment platform with adjustable hinges. In our approach, magnetorheological rotary brakes are substituted for the joints of a frame structure to simulate the nonlinear material behaviors of plastic hinges. For vibration control, a separate magnetorheological damper was employed to provide semi-active damping force to the nonlinear structure. A dynamic neural network was designed as a state observer to enable the feedback based semi-active vibration control. Based on the dynamic neural network observer, an adaptive fuzzy sliding mode based output control was developed for the magnetorheological damper to suppress the vibrations of the structure. The performance of the intelligent control algorithm was studied by subjecting the structure to shake table experiments. Experimental results show that the magnetorheological rotary brake can simulate the nonlinearity of the structural model with good repeatability. Moreover, different nonlinear behaviors can be achieved by controlling the input voltage of magnetorheological rotary damper. Different levels of nonlinearity in the vibration response of the structure can be achieved with the above adaptive fuzzy sliding mode control algorithm using a dynamic neural network observer.